Entropy Production in Dissipationless Hydrodynamics with an order parameter

We study hydrodynamics coupled to order parameter based on linear sigma model. We obtain numerical solutions for both boost invariant and non-boost invariant solutions. Both solutions show the order parameter rises with oscillations, which persist at late time. The temperature drops with correlated oscillations, which can be approximated by a power law at mid-rapidity. We also find the entropy is conserved in the boost invariant case, but entropy production is seen in non-boost invariant solution. We interpret the entropy production as due to smoothening of inhomogeneity in the off-equilibrium state.